The cluster expansion is a fundamental tool in mathematical physics that has many fruitful connections to other domains of mathematics, e.g., the Lovasz Local Lemma. In this talk I'll introduce abstract polymer models and the cluster expansion for their partition functions, and show how the cluster expansion yields efficient deterministic counting algorithms if the polymer model satisfies certain conditions. I will give an application of this framework to the Potts and hard-core models on expander graphs at low temperature. Based on joint works with T. Helmuth, G. Regts, M. Jenssen, and P. Keevash.